Timeline for Understanding a "straightforward" application of the method of stationary phase for proving a trace formula on compact hyperbolic surfaces
Current License: CC BY-SA 4.0
4 events
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| Nov 25 at 18:52 | comment | added | Asaf | I would say it is more of "non stationary phase"/orthogonality. One clearly needs to integrate $d\mu$ (as the result is $t$ dependent). Now we see that when one fixes the $t$ value to the be value of Busemann cocycle (which will give you the length of the geodesic), it fixes $\mu$ also by orthogonality. The rest of $dzdb$ computation is basically verbatim as the regular computation of the orbital integral | |
| Aug 6 at 2:58 | comment | added | Dmitrii Korshunov | >"the" prime geodesic< Since the surface is compact, every element of $\Gamma$ is hyperbolic. Also, any centralizer is a cyclic subgroup. From it it is easy to see in the upper half-plane model, after transforming the axis of the centralizer into a vertical line, that $F_\gamma$ is a domain between two concentric semi-circles and the prime geodesic is indeed unique [namely the part of the vertical line in the domain], any other geodesic segment will not glue up in the quotient. | |
| Aug 4 at 5:43 | history | edited | Daniele Tampieri | CC BY-SA 4.0 |
Added some more detail to the reference paper
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| Aug 3 at 23:25 | history | asked | Tsein32 | CC BY-SA 4.0 |